Download Determination of the pKa Value of Phenolphthalein by Means of

Creative Education, 2010, 2, 130-133
doi:10.4236/ce.2010.12020 Published Online September 2010 (http://www.SciRP.org/journal/ce)
Determination of the pKa Value of
Phenolphthalein by Means of Absorbance
Measurements
Manuel Alonso, Sebastián P. Chapela, María L. Cristaldo,
Inés Nievas, Hilda I. Burgos Oliver Gamondi, Carlos A. Stella
Departamento de Bioquímica Humana, Facultad de Medicina, Universidad de Buenos Aires, Paraguay 2155 Piso 5, 1121 Buenos
Aires, Argentina.
Email: [email protected]
Received July 23rd, 2010; revised August 11th, 2010; accepted August 27th, 2010.
ABSTRACT
We here report a laboratory protocol for the determination of the pKa value of an acid by means of determinations obtained with a spectrophotometer. Students determine the acidity constant (Ka) and the pKa associated with phenolphthalein from the absorbance values obtained from phenolphthalein solutions at different pHs. The present protocol
for the determination of the pKa takes a very short time and is useful when teaching in conditions with limited equipment.
Keywords: Medical Science Teaching
1. Introduction
Knowing the acidity constant value (Ka) [1] of an acid
and its associated pKa value is important for a medical
student for different reasons.
One of these reasons is that the pKa of a drug allows
obtaining its values of absorption, bioreactivity and tissular
accumulation as a function of the pH of the medium [2].
Another reason is that the pKa values of the amino acids
of a polypeptide chain are related to the function and
structure of the protein [3]. In addition, the pKa values of
different chemical species account for their tubular reabsorption if they are eliminated through the urine [4].
They also allow the understanding and management of
the internal medium of a living system [4,5], which can
be useful in the diagnosis or treatment of diseases.
Despite the importance of Ka and pKa, many students
of Biology or Health Sciences learn about them only
through lectures or exercises.
Previous studies [6] have shown that students are
usually not able to identify examples or topics that
arouse their interest. They have a poor qualitative management of the aspects of chemical balance, probably
because today’s teaching insists on an operational view
of the concept [6]. Many students are not able to infer
that the constant depends on the temperature and most of
Copyright © 2010 SciRes.
them believe that the constant depend on the concentration of the substances [6,7].
We believe that if the student could empirically determine the Ka value and thus the pKa of a substance, he /
she could better understand the basis of the acid-base
equilibrium and thus have a more open-minded criterion
about its application in practical situations.
The pKa of a certain chemical species can be empirically determined using the potentiometric technique by
measuring the pH value in a titration until it remains
constant [8,9]. However, both the titration and measurement of the pH are difficult because they take a relatively
long time, and courses in our University have too many
students and the equipment is usually not enough for all
the students.
For this reason, we have designed a practical way to
determine the pKa, which requires only the use of a
spectrophotometer or photocolorimeter. The main advantages of this technique are that it is sensitive, takes a
short time, and the equipments are both inexpensive and
user-friendly.
While there have been several experimental articles
published in education papers applying spectroscopy to
determine the pKa of acid-base indicators [10,11], the
present article addresses the question of how to give stuCE
Determination of the pKa Value of Phenolphthalein by Means of Absorbance Measurements
dents laboratory experience with limited equipment and
space.
In the protocol here presented, the student can determine the acidity constant (Ka) of phenolphthalein and its
associated pKa from absorbance values obtained from
solutions of this substance.
2. Theoretical Basis
The student must first know that the acid-base indicators
present different colors according to the pH of the medium. In the case of phenolphthalein, which is a weak
acid, its non-disassociated form has no color, whereas its
ionized form, or conjugate base, absorbs light at a wavelength of 550 nm.
The theoretical foundation (1) is based on the definition of the acidity constant:
Ka = H+ x A- / HA
(1)
where [HA] represents the concentration of the
non-disassociated acid, A- the concentration of its conjugated base, and H+ the concentration of protons.
In a strongly basic medium, most of the HA is as an Aanion because the concentration of non-disassociated
acid is much lower:
HA total = A-b
(2)
The supra-index “b” accounts for the alkalinity of the
medium.
In conditions in which the non-disassociated acid concentration is not negligible, the acid (HA total) will be
present in both its dissociated and non-disassociated
forms.
Taking Equation (2) into account, we can state that:
A-b = HA + A-
(3)
By Lambert-Beer Law, the Absorbance (Abs) of a solution is related to the concentration as follows:
Abs = α x b x A-
(4)
where
α = coefficient of molar absorption,
b = the distance traveled by the light beam.
Taking Equation (3) into consideration:
A-b – A- = HA
(8)
Finally, by removing the parenthesis:
H+ = Ka x Absb / Abs – Ka
(9)
This equation is similar to that of a straight line of the
following form:
y=a+bx
where:
y = H+
b = Ka x Absb
x = 1 / Abs
a = Ka
3. Development
The assays to carry out this protocol require 2 h at the
laboratory.
Before performing the dilutions or the absorbance
reading, the laboratory instructor should explain the basis
of the determination.
Instructor’s activity: the laboratory instructor should
prepare six solutions of Na2HPO4 (Mr = 142) 100 mM
with different values of pH. The solutions must be prepared from this mother solution and then add PO4-3
NaOH or HCl, as indicated in Table 1.
Each student then receives 10 ml of the solutions 1
to 6.
In addition, the instructor should prepare a phenolphthalein solution 1% in ethanol and dilutes a 200-l
aliquot in 10 ml water. Each student receives 6 ml of this
dilution.
Student’s activity: each student or group of students
mixes 10 ml of each phosphate solution with 1 ml of the
diluted phenolphthalein solution. These six new solutions
must be denominated as A, B, C, D, E and F. The absorbance of the solutions is read at 550 nm in a spectrophotometer or photocolorimeter. The student will then
record the values obtained and the pH value for each
solution in a table.
(5)
Ka = H+ x A- / A-b – A-
Considering Equation (4)
Ka = H+ x (Abs / α x b) / (Absb / α x b – Abs / α x b) (6)
Then, by removing the common factor α x b and simplifying the equation, we obtain:
Copyright © 2010 SciRes.
H+ = Ka x (Absb / Abs – 1)
Table 1. Solutions with different pH that the laboratory
instructor should prepare.
And then, by replacing (5) in (1), we obtain:
Ka = H+ x Abs / (Absb – Abs)
Clearing H+, we have:
131
(7)
Solution
Volume of NaOH
1 M every 10 ml of
phosphate (l)
Volume of HC (c)
every 10 ml of
phosphate (l)
pH value
obtained
1
40
---
9.36
2
10
---
9.23
3
---
---
9.15
4
---
10
8.87
5
---
20
8.73
6
---
30
8.56
CE
132
Determination of the pKa Value of Phenolphthalein by Means of Absorbance Measurements
4. Results
5. Conclusions
After measuring the absorbance of the A, B, C, D, E and
F solutions, the values of “y” and “x” should also be recorded and calculated. The values of a representative
assay we carried out are presented in Table 2. Figure 1
shows a graphic representation of the values of Table 2.
After that, “a” (the point at which the line crosses the y
axis) is calculated in the two following possible ways:
a) graphically, by drawing the straight line manually in
a millimeter paper and making the line as close as possible to all the points. With this procedure, the Ka showed
values of 2.75 –10 and 3.25 –10, which represented values
of 9.6 and 9.5 respectively.
b) by adjusting the data with the program Origin®
(version 6.0). This procedure yielded a Ka = 4.657 –10 (
1.132 –10), which corresponds to a pKa value of 9.3  0.1.
It must be pointed out that the pKa accepted for phenolphtalein at 25˚C is 9, 7 [12].
This protocol allows students to determine the pKa value
of phenolphthalein in a short time and without using the
potentiometric method. It thus has the advantage that, in
a laboratory where a spectrophotometer or photocolorimeter are available, a large number of students can
carry out the determination at the same time. As we mentioned in Introduction there are many good procedures
but may not be useful for large classes with limited
equipment.
This makes it easier to develop the activity, especially
because the use of a potentiometric method requires numerous pH-meters, takes a long time and depends on the
ability of the students. In addition, the laboratory instructor is able to show the application of the Lambert-Beer Law for acid-base indicators in which the
forms have different coloration according to the pH of
the medium.
This strategy for the determination of the pKa can also
be used to discuss the case of other chemical species in
which the non-ionized form has color [13]. In such case,
the contribution of the color of the other form of the
weak acid should be subtracted from the absorbance
measured in Table 2.
Table 2. Absorbance (Abs) values of the indicator solutions
at different pHs.
Representative assay.
y = H+
Abs
x = 1 / Abs
A
4.36 10
–10
0.411
2.433
B
5.89 10 –10
0.306
3.268
C
7.08 10 –10
0.270
3.704
D
1.35 10 –9
0.109
9.174
E
1.86 10
–9
0.041
24.390
F
2.75 10 –9
0.026
38.462
Solution
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3,00E-009
3,00E-009
2,50E-009
2,50E-009
(H+)
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2,00E-009
2,00E-009
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Figure 1. Graphic representation of the absorbance values
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indicates the [H+] from which the pKa is calculated according to Equation (9).
Copyright © 2010 SciRes.
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Determination of the pKa Value of Phenolphthalein by Means of Absorbance Measurements
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Copyright © 2010 SciRes.
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